The monastery is visible from a distance because of the massiveness of the church, strongly characterized by the polygonal drums and conical roofs of its two domes. There are several chapels nearby: three on the hills east of the stream, one approximately 3 km south of the monastery on the road to Bastam, and another that serves as the church for the village of Ghara-Kilise.[4]

Not much appears to remain of the original church, which was extensively rebuilt in 1329 after an earthquake damaged the structure in 1319. Nevertheless, some of the parts surrounding the altar apse date from the 10th century.

Much of the present structure dates from 1811 [5] when Qajar prince Abbas Mirza helped in renovations and repairs. Undertaken by Simeon, Father Superior of the monastery, a large narthex-like western extension was added to the medieval church. This structure exactly duplicates the design of the cathedral at Etchmiadzin.[6] The 19th century additions are from carved sandstone. The earliest parts are of black and white stone, hence its Turkic name Kara Kilise, the Black Church.

A fortified wall surrounds the church and its now-abandoned monastery buildings.

In July 2008, the St. Thaddeus monastery was added to UNESCO's World Heritage List, along with two other Armenian monuments located in the same province: Saint Stepanos Monastery and the chapel of Dzordzor.

According to Armenian Church tradition, the Apostles Thaddeus and Bartholomew traveled through Armenia in AD 45 to preach the word of God; many people were converted and numerous secret Christian communities were established there.

The ancient Christian historian Moses of Khorene tell the following story, considered a legend by most modern historiography.[7] Thaddeus converted King Abgar V of Edessa. After his death, the Armenian kingdom was split into two parts. His son Ananun crowned himself in Edessa, while his nephew Sanatruk ruled in Armenia. About AD 66, Ananun gave the order to kill St. Thaddeus in Edessa. The king's daughter Sandokht, who had converted to Christianity, was martyred with Thaddeus. Her tomb is said to be located near the Ghara Kelisa.